Bleaching of medium consistency paper pulp with ozone has only recently become possible and is described in more detail in pending U.S. applications Ser. No. 693,287 filed Apr. 30, 1991 and Ser. No. 498,205 filed Mar. 23, 1991, the entire content of both of which applications is incorporated herein by reference. Previous draw backs, e.g. the high cost of ozone, the known disadvantages associated with operating at either low consistency (less than about 5%) or at very high consistency (above about 25%) and the fact that ozone readily attacks the carbohydrates of the pulp, have now been overcome. Due to the present invention the efficiency of an ozone bleaching operation of medium consistency pulp, i.e. a cellulosic fiber suspension having a consistency of from about 5 to about 20 percent, is further increased by incorporation of an additional chemical feeding step into the ozone bleaching stage.